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arXiv · 2212.11718

On the REM approximation of TAP free energies

Nicola Kistler·Marius Alexander Schmidt·Giulia Sebastiani
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Abstract

The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical large deviations treatment. This allows to identify the origin of the physically unsettling quadratic (in the inverse of temperature) correction to the Parisi free energy for the SK-model, and formalizes the $\textit{true}$ cavity dynamics which acts on TAP-space, i.e. on the space of TAP-solutions. From a non-spin glass point of view, this work is the first in a series of refinements which addresses the stability of hierarchical structures in models of evolving populations.

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Nicola Kistler, Marius Alexander Schmidt, Giulia Sebastiani. 2022-12-22. On the REM approximation of TAP free energies. https://doi.org/10.1088/1751-8121%2Facdf30

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